L7.Solving Rational Equations by Cross Multiplying

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Date: __________________

Solving Rational Equations by Cross Multiplying Algebra 1

Rational equations, or equations that involve one or more rational expressions, occur often in mathematics. It is important to be able to solve them. When we have an equation where a fraction is equal to another fraction, called a proportion, we can solve them by using the common technique called cross-multiplying.

Exercise #1: Solve for x in each of following equations. Check your answers by using the STORE feature on your calculator.

1. x = 7 93

2. x - 5 = 4 15 5

3. 3x + 1 = 5 x -1

4. x - 6 = -2x - 2

3

15

5. 6 = 3 3x -1 4

6. 5 = 7 x x-4

Algebra 1, Unit #7 ? Rational Algebra ? L7 The Arlington Algebra Project, LaGrangeville, NY 12540

Exercise #2: The denominator of an unreduced fraction is 8 less than the numerator of the fraction. The reduced form of the fraction is 5 . Find the original unreduced fraction.

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Exercise #3: The numerator and denominator of a fraction are in the ratio 2:3. When the numerator is increased by 1 and the denominator is decreased by 1, the value of the new fraction is 5 . Find the

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original fraction.

Exercise #4: Solve each equation for all values of x. (a) x + 3 = 15

x +1 x +7

(b) x - 1 = 2x - 2 7 3x - 1

Algebra 1, Unit #7- Rational Algebra ? L7 The Arlington Algebra Project, LaGrangeville, NY 12540

Name: ____________________________________

Date: __________________

Skills

Solving Rational Equations by Cross Multiplying Algebra 1 Homework

Solve for the value of x in each equation. Check your answers using STORE or a TABLE.

1. 12 = 24 x x+5

2. x - 3 = x + 5 5 15

3.

2 3x - 4

=

1 4

4.

5x x +1

=

4

5. 3 = 1 5- 3x 2

6. 3 = 2 x 5- x

7. 2 = 5 x 3x -1

8. 12 = 15 2-x 7+x

Algebra 1, Unit #7 ? Rational Algebra ? L7 The Arlington Algebra Project, LaGrangeville, NY 12540

9. The numerator and denominator of a fraction are in the ratio 1:2. When the numerator is decreased by 2 and the denominator is multiplied by 2, the value of the new fraction is 3 . Find the original

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fraction.

Solve each of the following for all values of x. Check your answers using STORE.

10. x + 1 = 3x + 3 x 4x -2

11. x + 2 = 2x + 4 x-2 x+1

Reasoning ? The most important rule when manipulating an equation is to always do the same

operation to both sides of the equation. In the next exercise we will see why cross-multiplying works. 12. Consider the general rational equation a = c .

bd (a) What equation results if you multiply both sides of this equation by bd ?

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(b) What does the expression bd represent in the equation above?

Algebra 1, Unit #7- Rational Algebra ? L7 The Arlington Algebra Project, LaGrangeville, NY 12540

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